{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"http://hilpisch.com/tpq_logo.png\" alt=\"The Python Quants\" width=\"45%\" align=\"right\" border=\"4\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Interest Rate Swaps"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Very nascent*."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Interest rate swaps are a first step towards including **rate-sensitive instruments** in the modeling and valuation spectrum of DX Analytics. The model used in the following is the **square-root diffusion process** by Cox-Ingersoll-Ross (1985). Data used are UK/London OIS and Libor rates."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import dx\n",
    "import time\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import datetime as dt\n",
    "from pylab import plt\n",
    "plt.style.use('seaborn')\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## OIS Data & Discounting"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We start by importing **OIS term structure data** (source: http://www.bankofengland.co.uk) for risk-free discounting. We also adjust the data structure somewhat for our purposes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# UK OIS Spot Rates Yield Curve\n",
    "oiss = pd.read_excel('data/ukois09.xls', 'oiss')\n",
    "# use years as index\n",
    "oiss = oiss.set_index('years')\n",
    "# del oiss['years']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# only date information for columns, no time\n",
    "oiss.columns = [d.date() for d in oiss.columns]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>2014-10-01</th>\n",
       "      <th>2014-10-02</th>\n",
       "      <th>2014-10-03</th>\n",
       "      <th>2014-10-06</th>\n",
       "      <th>2014-10-07</th>\n",
       "      <th>2014-10-08</th>\n",
       "      <th>2014-10-09</th>\n",
       "      <th>2014-10-10</th>\n",
       "      <th>2014-10-13</th>\n",
       "      <th>2014-10-14</th>\n",
       "      <th>2014-10-15</th>\n",
       "      <th>2014-10-16</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>years</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>4.666667</th>\n",
       "      <td>1.550947</td>\n",
       "      <td>1.525838</td>\n",
       "      <td>1.570203</td>\n",
       "      <td>1.533901</td>\n",
       "      <td>1.479044</td>\n",
       "      <td>1.445234</td>\n",
       "      <td>1.436023</td>\n",
       "      <td>1.409962</td>\n",
       "      <td>1.337567</td>\n",
       "      <td>1.283932</td>\n",
       "      <td>1.063205</td>\n",
       "      <td>1.234125</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4.750000</th>\n",
       "      <td>1.563661</td>\n",
       "      <td>1.538616</td>\n",
       "      <td>1.583198</td>\n",
       "      <td>1.546459</td>\n",
       "      <td>1.491152</td>\n",
       "      <td>1.457593</td>\n",
       "      <td>1.448627</td>\n",
       "      <td>1.422015</td>\n",
       "      <td>1.349782</td>\n",
       "      <td>1.296052</td>\n",
       "      <td>1.074773</td>\n",
       "      <td>1.246277</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4.833333</th>\n",
       "      <td>1.576142</td>\n",
       "      <td>1.551158</td>\n",
       "      <td>1.595952</td>\n",
       "      <td>1.558789</td>\n",
       "      <td>1.503050</td>\n",
       "      <td>1.469768</td>\n",
       "      <td>1.461040</td>\n",
       "      <td>1.433887</td>\n",
       "      <td>1.361832</td>\n",
       "      <td>1.308025</td>\n",
       "      <td>1.086254</td>\n",
       "      <td>1.258307</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4.916667</th>\n",
       "      <td>1.588400</td>\n",
       "      <td>1.563474</td>\n",
       "      <td>1.608472</td>\n",
       "      <td>1.570898</td>\n",
       "      <td>1.514746</td>\n",
       "      <td>1.481764</td>\n",
       "      <td>1.473269</td>\n",
       "      <td>1.445585</td>\n",
       "      <td>1.373724</td>\n",
       "      <td>1.319859</td>\n",
       "      <td>1.097650</td>\n",
       "      <td>1.270219</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5.000000</th>\n",
       "      <td>1.600442</td>\n",
       "      <td>1.575572</td>\n",
       "      <td>1.620768</td>\n",
       "      <td>1.582794</td>\n",
       "      <td>1.526247</td>\n",
       "      <td>1.493588</td>\n",
       "      <td>1.485320</td>\n",
       "      <td>1.457116</td>\n",
       "      <td>1.385461</td>\n",
       "      <td>1.331557</td>\n",
       "      <td>1.108962</td>\n",
       "      <td>1.282014</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          2014-10-01  2014-10-02  2014-10-03  2014-10-06  2014-10-07  \\\n",
       "years                                                                  \n",
       "4.666667    1.550947    1.525838    1.570203    1.533901    1.479044   \n",
       "4.750000    1.563661    1.538616    1.583198    1.546459    1.491152   \n",
       "4.833333    1.576142    1.551158    1.595952    1.558789    1.503050   \n",
       "4.916667    1.588400    1.563474    1.608472    1.570898    1.514746   \n",
       "5.000000    1.600442    1.575572    1.620768    1.582794    1.526247   \n",
       "\n",
       "          2014-10-08  2014-10-09  2014-10-10  2014-10-13  2014-10-14  \\\n",
       "years                                                                  \n",
       "4.666667    1.445234    1.436023    1.409962    1.337567    1.283932   \n",
       "4.750000    1.457593    1.448627    1.422015    1.349782    1.296052   \n",
       "4.833333    1.469768    1.461040    1.433887    1.361832    1.308025   \n",
       "4.916667    1.481764    1.473269    1.445585    1.373724    1.319859   \n",
       "5.000000    1.493588    1.485320    1.457116    1.385461    1.331557   \n",
       "\n",
       "          2014-10-15  2014-10-16  \n",
       "years                             \n",
       "4.666667    1.063205    1.234125  \n",
       "4.750000    1.074773    1.246277  \n",
       "4.833333    1.086254    1.258307  \n",
       "4.916667    1.097650    1.270219  \n",
       "5.000000    1.108962    1.282014  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "oiss.tail()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we replace the **year fraction index** by a **DatetimeIndex**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# generate time index given input data\n",
    "# starting date + 59 months\n",
    "date = oiss.columns[-1]\n",
    "index = pd.date_range(date, periods=60, freq='M') # , tz='GMT')\n",
    "index = [d.replace(day=date.day) for d in index]\n",
    "index = pd.DatetimeIndex(index)\n",
    "oiss.index = index"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us have a look at the **most current data**, i.e. the term structure, of the data set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x10ba062b0>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Ui65cOJ6dlc4jK6axZkEJGemOLZCk/s4QJfWCWDzBht0neGl7BbF4gllTR/Gd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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b9b2898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "oiss.iloc[:, -1].plot(figsize=(10, 6))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This data is used to instantiate a `deterministic_short_rate` **model for risk-neutral discounting** purposes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# generate deterministic short rate model based on UK OIS curve\n",
    "ois = dx.deterministic_short_rate('ois', list(zip(oiss.index, oiss.iloc[:, -1].values / 100)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([0.989825148692371, 0.9922754901627036, 0.9956237774158325, 1.0],\n",
       " array([datetime.datetime(2015, 1, 31, 0, 0),\n",
       "        datetime.datetime(2015, 7, 31, 0, 0),\n",
       "        datetime.datetime(2016, 1, 31, 0, 0),\n",
       "        datetime.datetime(2016, 7, 31, 0, 0)], dtype=object))"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# example dates and corresponding discount factors\n",
    "dr = pd.date_range('2015-1', periods=4, freq='6m').to_pydatetime()\n",
    "ois.get_discount_factors(dr)[::-1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Libor Market Data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We want to model a **3 month Libor-based interest rate swap**. To this end, we need Libor term structure data, i.e. forward rates in this case (source: http://www.bankofengland.co.uk), to calibrate the  valuation to. The data importing and adjustments are the same as before."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# UK Libor foward rates\n",
    "libf = pd.read_excel('data/ukblc05.xls', 'fwds')\n",
    "# use years as index\n",
    "libf = libf.set_index('years')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# only date information for columns, no time\n",
    "libf.columns = [d.date() for d in libf.columns]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>2014-10-01</th>\n",
       "      <th>2014-10-02</th>\n",
       "      <th>2014-10-03</th>\n",
       "      <th>2014-10-06</th>\n",
       "      <th>2014-10-07</th>\n",
       "      <th>2014-10-08</th>\n",
       "      <th>2014-10-09</th>\n",
       "      <th>2014-10-10</th>\n",
       "      <th>2014-10-13</th>\n",
       "      <th>2014-10-14</th>\n",
       "      <th>2014-10-15</th>\n",
       "      <th>2014-10-16</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>years</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>4.666667</th>\n",
       "      <td>2.722915</td>\n",
       "      <td>2.686731</td>\n",
       "      <td>2.678433</td>\n",
       "      <td>2.681385</td>\n",
       "      <td>2.639166</td>\n",
       "      <td>2.542012</td>\n",
       "      <td>2.528768</td>\n",
       "      <td>2.489063</td>\n",
       "      <td>2.470154</td>\n",
       "      <td>2.349732</td>\n",
       "      <td>2.372435</td>\n",
       "      <td>2.157431</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4.750000</th>\n",
       "      <td>2.733588</td>\n",
       "      <td>2.697887</td>\n",
       "      <td>2.690366</td>\n",
       "      <td>2.692824</td>\n",
       "      <td>2.650841</td>\n",
       "      <td>2.554583</td>\n",
       "      <td>2.543066</td>\n",
       "      <td>2.502357</td>\n",
       "      <td>2.483842</td>\n",
       "      <td>2.366052</td>\n",
       "      <td>2.387671</td>\n",
       "      <td>2.176186</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4.833333</th>\n",
       "      <td>2.744126</td>\n",
       "      <td>2.708848</td>\n",
       "      <td>2.702083</td>\n",
       "      <td>2.704147</td>\n",
       "      <td>2.662380</td>\n",
       "      <td>2.567071</td>\n",
       "      <td>2.557216</td>\n",
       "      <td>2.515531</td>\n",
       "      <td>2.497446</td>\n",
       "      <td>2.382298</td>\n",
       "      <td>2.402829</td>\n",
       "      <td>2.194784</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4.916667</th>\n",
       "      <td>2.754540</td>\n",
       "      <td>2.719634</td>\n",
       "      <td>2.713604</td>\n",
       "      <td>2.715368</td>\n",
       "      <td>2.673794</td>\n",
       "      <td>2.579486</td>\n",
       "      <td>2.571229</td>\n",
       "      <td>2.528592</td>\n",
       "      <td>2.510973</td>\n",
       "      <td>2.398468</td>\n",
       "      <td>2.417915</td>\n",
       "      <td>2.213221</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5.000000</th>\n",
       "      <td>2.764842</td>\n",
       "      <td>2.730264</td>\n",
       "      <td>2.724949</td>\n",
       "      <td>2.726501</td>\n",
       "      <td>2.685095</td>\n",
       "      <td>2.591835</td>\n",
       "      <td>2.585117</td>\n",
       "      <td>2.541548</td>\n",
       "      <td>2.524432</td>\n",
       "      <td>2.414562</td>\n",
       "      <td>2.432939</td>\n",
       "      <td>2.231493</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          2014-10-01  2014-10-02  2014-10-03  2014-10-06  2014-10-07  \\\n",
       "years                                                                  \n",
       "4.666667    2.722915    2.686731    2.678433    2.681385    2.639166   \n",
       "4.750000    2.733588    2.697887    2.690366    2.692824    2.650841   \n",
       "4.833333    2.744126    2.708848    2.702083    2.704147    2.662380   \n",
       "4.916667    2.754540    2.719634    2.713604    2.715368    2.673794   \n",
       "5.000000    2.764842    2.730264    2.724949    2.726501    2.685095   \n",
       "\n",
       "          2014-10-08  2014-10-09  2014-10-10  2014-10-13  2014-10-14  \\\n",
       "years                                                                  \n",
       "4.666667    2.542012    2.528768    2.489063    2.470154    2.349732   \n",
       "4.750000    2.554583    2.543066    2.502357    2.483842    2.366052   \n",
       "4.833333    2.567071    2.557216    2.515531    2.497446    2.382298   \n",
       "4.916667    2.579486    2.571229    2.528592    2.510973    2.398468   \n",
       "5.000000    2.591835    2.585117    2.541548    2.524432    2.414562   \n",
       "\n",
       "          2014-10-15  2014-10-16  \n",
       "years                             \n",
       "4.666667    2.372435    2.157431  \n",
       "4.750000    2.387671    2.176186  \n",
       "4.833333    2.402829    2.194784  \n",
       "4.916667    2.417915    2.213221  \n",
       "5.000000    2.432939    2.231493  "
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "libf.tail()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# generate time index given input data\n",
    "# starting date + 59 months\n",
    "date = libf.columns[-1]\n",
    "index = pd.date_range(date, periods=60, freq='M')  # , tz='GMT')\n",
    "index = [d.replace(day=date.day) for d in index]\n",
    "index = pd.DatetimeIndex(index)\n",
    "libf.index = index"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And the short end of the **Libor term sturcture** visualized."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x10bfe8198>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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kjoWjWDIjj6z0JLdLFOl3FK5ERGKQPxBkW0k1b205ycnqJgBG5qSzfHY+t143lvpzLS5X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\nIuj/AGO0EYAY4TkZAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10bfb5940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "libf.iloc[:, -1].plot(figsize=(10, 6))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model Calibration"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, equipped with the Libor data, we calibrate the **square-root diffusion short rate model**. A bit of data preparation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "t = libf.index.to_pydatetime()\n",
    "f = libf.iloc[:, -1].values / 100\n",
    "initial_value = 0.005"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A **mean-squared error (MSE)** function to be minimized during calibration."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def srd_forward_error(p0):\n",
    "    global initial_value, f, t\n",
    "    if p0[0] < 0 or p0[1] < 0 or p0[2] < 0:\n",
    "        return 100\n",
    "    f_model = dx.srd_forwards(initial_value, p0, t)\n",
    "    MSE = np.sum((f - f_model) ** 2) / len(f)\n",
    "    return MSE"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And the **calibration** itself."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.optimize import fmin"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 0.000000\n",
      "         Iterations: 371\n",
      "         Function evaluations: 649\n"
     ]
    }
   ],
   "source": [
    "opt = fmin(srd_forward_error, (1.0, 0.7, 0.2),\n",
    "           maxiter=1000, maxfun=1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The **optimal parameters** (kappa, theta, sigma) are:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.00544441, 1.80697228, 0.23689443])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "opt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The **model fit** is not too bad in this case."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x10bfbcef0>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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M3gZo6wmRxlIQExGRY/L6fHyXsYdZK7LZWvvqoc7RYYwfmsCoAV3okRhDYWEJ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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10badc940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 6))\n",
    "plt.plot(t, f, label='market forward rates')\n",
    "plt.plot(t, dx.srd_forwards(initial_value, opt, t), 'r.', label='model forward rates')\n",
    "plt.gcf().autofmt_xdate(); plt.legend(loc=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Floating Rate Modeling"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The optimal parameters from the calibration are used to model the **floating rate (3m Libor rate)**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "# market environment\n",
    "me_srd = dx.market_environment('me_srd', dt.datetime(2014, 10, 16))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "# square-root diffusion\n",
    "me_srd.add_constant('initial_value', 0.02)\n",
    "me_srd.add_constant('kappa', opt[0]) \n",
    "me_srd.add_constant('theta', opt[1])\n",
    "me_srd.add_constant('volatility', opt[2])\n",
    "me_srd.add_curve('discount_curve', ois)\n",
    "  # OIS discounting object\n",
    "me_srd.add_constant('currency', 'EUR')\n",
    "me_srd.add_constant('paths', 10000)\n",
    "me_srd.add_constant('frequency', 'w')\n",
    "me_srd.add_constant('starting_date', me_srd.pricing_date)\n",
    "me_srd.add_constant('final_date', dt.datetime(2020, 12, 31))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "srd = dx.square_root_diffusion('srd', me_srd)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us have a look at some **simulated rate paths**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "paths = srd.get_instrument_values()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10ba7de10>,\n",
       " <matplotlib.lines.Line2D at 0x10c2f6400>,\n",
       " <matplotlib.lines.Line2D at 0x10c2f6668>,\n",
       " <matplotlib.lines.Line2D at 0x10c2f6898>,\n",
       " <matplotlib.lines.Line2D at 0x10c2f6ac8>,\n",
       " <matplotlib.lines.Line2D at 0x10c2f6cf8>]"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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2jmxK5wUnx9fdf3TaFyam5ZDPJtfdD5DPGACs9DliZphU6xaO4zI1ouA4fuuB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\nx7hMVBIpGpafNN9E7vKdgqdadfMzVkp+qc+PFQhT09vIVX2FuX33yoL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geQu7i+KRrflE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HPMTuVquDdGJqFyYaaE67ro1WsAXuexKCMqaaqFRdzZEsNtDQG3O/aVqz0K13V9crX6Dn40Powo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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10badc240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 6))\n",
    "plt.plot(srd.time_grid, paths[:, :6])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Interest Rate Swap"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we can model the **interest rate swap** itself."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Modeling"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, the market environment with all the **parameters** needed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "# market environment for the IRS\n",
    "me_irs = dx.market_environment('irs', me_srd.pricing_date)\n",
    "me_irs.add_constant('fixed_rate', 0.01)\n",
    "me_irs.add_constant('trade_date', me_srd.pricing_date)\n",
    "me_irs.add_constant('effective_date', me_srd.pricing_date)\n",
    "me_irs.add_constant('payment_date', dt.datetime(2014, 12, 27))\n",
    "me_irs.add_constant('payment_day', 27)\n",
    "me_irs.add_constant('termination_date', me_srd.get_constant('final_date'))\n",
    "me_irs.add_constant('currency', 'EUR')\n",
    "me_irs.add_constant('notional', 1000000)\n",
    "me_irs.add_constant('tenor', '6m')\n",
    "me_irs.add_constant('counting', 'ACT/360')\n",
    "# discount curve from mar_env of floating rate"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The instantiation of the **valuation object**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "irs = dx.interest_rate_swap('irs', srd, me_irs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Valuation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The **present value** of the interest rate swap given the assumption, in particular, of the fixed rate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 198 ms, sys: 82 ms, total: 280 ms\n",
      "Wall time: 299 ms\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "482804.6280483039"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%time irs.present_value(fixed_seed=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can also generate a **full output of all present values** per simulation path."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2014-12-27</th>\n",
       "      <td>20919.908406</td>\n",
       "      <td>3765.545880</td>\n",
       "      <td>-10000.000000</td>\n",
       "      <td>20447.662984</td>\n",
       "      <td>15671.171542</td>\n",
       "      <td>-461.905549</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-06-27</th>\n",
       "      <td>27796.391566</td>\n",
       "      <td>67649.371268</td>\n",
       "      <td>-7952.865109</td>\n",
       "      <td>21069.238749</td>\n",
       "      <td>6547.642190</td>\n",
       "      <td>56254.997722</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-12-27</th>\n",
       "      <td>72797.267752</td>\n",
       "      <td>65085.851729</td>\n",
       "      <td>-9495.534310</td>\n",
       "      <td>7184.517383</td>\n",
       "      <td>-6249.109421</td>\n",
       "      <td>72603.409748</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-06-27</th>\n",
       "      <td>146587.773739</td>\n",
       "      <td>60725.900678</td>\n",
       "      <td>-9450.695252</td>\n",
       "      <td>10630.874710</td>\n",
       "      <td>1457.279233</td>\n",
       "      <td>96390.826927</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-12-27</th>\n",
       "      <td>112006.856512</td>\n",
       "      <td>11685.574401</td>\n",
       "      <td>-9365.011855</td>\n",
       "      <td>36777.060898</td>\n",
       "      <td>40752.233786</td>\n",
       "      <td>42437.807055</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-06-27</th>\n",
       "      <td>89091.008350</td>\n",
       "      <td>19143.973791</td>\n",
       "      <td>-8652.442452</td>\n",
       "      <td>10394.933700</td>\n",
       "      <td>81112.588234</td>\n",
       "      <td>49316.809090</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-12-27</th>\n",
       "      <td>153802.099096</td>\n",
       "      <td>37433.554707</td>\n",
       "      <td>-2231.031239</td>\n",
       "      <td>3046.024441</td>\n",
       "      <td>81218.496071</td>\n",
       "      <td>89235.982850</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-06-27</th>\n",
       "      <td>114033.046751</td>\n",
       "      <td>-4200.273599</td>\n",
       "      <td>8204.181410</td>\n",
       "      <td>86020.232903</td>\n",
       "      <td>92146.494366</td>\n",
       "      <td>44010.774119</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-12-27</th>\n",
       "      <td>165327.788708</td>\n",
       "      <td>-7186.102024</td>\n",
       "      <td>-8829.883386</td>\n",
       "      <td>46785.300398</td>\n",
       "      <td>171037.865434</td>\n",
       "      <td>14615.688086</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2019-06-27</th>\n",
       "      <td>101110.008932</td>\n",
       "      <td>-9038.246291</td>\n",
       "      <td>-6883.724709</td>\n",
       "      <td>29794.380064</td>\n",
       "      <td>183168.704902</td>\n",
       "      <td>-4599.638746</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2019-12-27</th>\n",
       "      <td>57890.028467</td>\n",
       "      <td>-8998.424023</td>\n",
       "      <td>-8573.907447</td>\n",
       "      <td>12491.846129</td>\n",
       "      <td>151080.678798</td>\n",
       "      <td>-8960.333669</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-06-27</th>\n",
       "      <td>95516.235053</td>\n",
       "      <td>-8968.295497</td>\n",
       "      <td>-8963.127240</td>\n",
       "      <td>15234.994497</td>\n",
       "      <td>67282.503413</td>\n",
       "      <td>-7763.697572</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-12-27</th>\n",
       "      <td>4651.947620</td>\n",
       "      <td>-4500.468014</td>\n",
       "      <td>-6316.280222</td>\n",
       "      <td>39899.010233</td>\n",
       "      <td>107971.761933</td>\n",
       "      <td>-8568.679338</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                        0             1             2             3  \\\n",
       "2014-12-27   20919.908406   3765.545880 -10000.000000  20447.662984   \n",
       "2015-06-27   27796.391566  67649.371268  -7952.865109  21069.238749   \n",
       "2015-12-27   72797.267752  65085.851729  -9495.534310   7184.517383   \n",
       "2016-06-27  146587.773739  60725.900678  -9450.695252  10630.874710   \n",
       "2016-12-27  112006.856512  11685.574401  -9365.011855  36777.060898   \n",
       "2017-06-27   89091.008350  19143.973791  -8652.442452  10394.933700   \n",
       "2017-12-27  153802.099096  37433.554707  -2231.031239   3046.024441   \n",
       "2018-06-27  114033.046751  -4200.273599   8204.181410  86020.232903   \n",
       "2018-12-27  165327.788708  -7186.102024  -8829.883386  46785.300398   \n",
       "2019-06-27  101110.008932  -9038.246291  -6883.724709  29794.380064   \n",
       "2019-12-27   57890.028467  -8998.424023  -8573.907447  12491.846129   \n",
       "2020-06-27   95516.235053  -8968.295497  -8963.127240  15234.994497   \n",
       "2020-12-27    4651.947620  -4500.468014  -6316.280222  39899.010233   \n",
       "\n",
       "                        4             5  \n",
       "2014-12-27   15671.171542   -461.905549  \n",
       "2015-06-27    6547.642190  56254.997722  \n",
       "2015-12-27   -6249.109421  72603.409748  \n",
       "2016-06-27    1457.279233  96390.826927  \n",
       "2016-12-27   40752.233786  42437.807055  \n",
       "2017-06-27   81112.588234  49316.809090  \n",
       "2017-12-27   81218.496071  89235.982850  \n",
       "2018-06-27   92146.494366  44010.774119  \n",
       "2018-12-27  171037.865434  14615.688086  \n",
       "2019-06-27  183168.704902  -4599.638746  \n",
       "2019-12-27  151080.678798  -8960.333669  \n",
       "2020-06-27   67282.503413  -7763.697572  \n",
       "2020-12-27  107971.761933  -8568.679338  "
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "irs.present_value(full=True).iloc[:, :6]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Copyright, License & Disclaimer**\n",
    "\n",
    "© Dr. Yves J. Hilpisch | The Python Quants GmbH\n",
    "\n",
    "DX Analytics (the \"dx library\" or \"dx package\") is licensed under the GNU Affero General\n",
    "Public License version 3 or later (see http://www.gnu.org/licenses/).\n",
    "\n",
    "DX Analytics comes with no representations or warranties, to the extent\n",
    "permitted by applicable law.\n",
    "\n",
    "http://tpq.io | [dx@tpq.io](mailto:team@tpq.io) |\n",
    "http://twitter.com/dyjh\n",
    "\n",
    "<img src=\"http://hilpisch.com/tpq_logo.png\" alt=\"The Python Quants\" width=\"35%\" align=\"right\" border=\"0\"><br>\n",
    "\n",
    "**Quant Platform** | http://pqp.io\n",
    "\n",
    "**Python for Finance Training** | http://training.tpq.io\n",
    "\n",
    "**Certificate in Computational Finance** | http://compfinance.tpq.io\n",
    "\n",
    "**Derivatives Analytics with Python (Wiley Finance)** |\n",
    "http://dawp.tpq.io\n",
    "\n",
    "**Python for Finance (2nd ed., O'Reilly)** |\n",
    "http://py4fi.tpq.io"
   ]
  }
 ],
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